Circle generation algorithm
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The document describes the Breshenham's circle generation algorithm. It explains that the algorithm uses a decision parameter to iteratively select pixels along the circumference of a circle. It provides pseudocode for the algorithm, which initializes x and y values, calculates a decision parameter, and increments x while decrementing y at each step, plotting points based on the decision parameter. An example of applying the algorithm to generate a circle with radius 5 is also provided.
Circle generation algorithm
- 1. Circle Generation Algorithm Total Slide (14)
- 2. Circle Generation Algorithm • Circle Generation is a tricky task for computer because we have to choose pixels along a circular path. • Selection of right pixel for illumination requires more computation time as compare to Line drawing algorithm. • Selection of appropriate pixels is based on decision parameter which is same as line drawing algorithm but computation is different. • Two algorithm for Circle generation are: • Breshenham’s Circle Generation Algorithm • Mid Point Circle generation Algorithm.
- 4. Breshenham’s Circle Generation Algorithm 1. Set x=0; y=10 here y contains value for radius of circle 2. p=3-(2*r) calculate first decision parameter which calculate which pixel will glow on the circumference of the circle. 3. Repeat setp 3 until (i<y), set always set i=x initially 4. If p<0 calculate x=x+1, Y=Y and next decision parameter by p=p+4*x+6; Otherwise Calculate y=y-1 and x=x+1; Calculate next decision parameter by p=p+4*x-4*y+10; calculte points for all octants of circle by using and paint corresponding points with color putpixel(xc+x,yc-y,4); putpixel(xc-x,yc-y,4); putpixel(xc+x,yc+y,4); putpixel(xc-x,yc+y,4); putpixel(xc+y,yc-x,4); putpixel(xc-y,yc-x,4); putpixel(xc+y,yc+x,4); putpixel(xc-y,yc+x,4); 5. Stop algorithm when (i>y) or (i==y)
- 5. Code section from circle Program • x=0;y=100; • p=3-(2*r); • for(int i=0;i<y;i++) • { • if(p<0) • { x=x+1; p=p+4*x+6; } • else { y=y-1; x=x+1; p=p+4*x-4*y+10; } • putpixel(xc+x,yc-y,4); putpixel(xc-x,yc-y,4); • putpixel(xc+x,yc+y,4); putpixel(xc-x,yc+y,4); • putpixel(xc+y,yc-x,4); putpixel(xc-y,yc-x,4); • putpixel(xc+y,yc+x,4); putpixel(xc-y,yc+x,4); • delay(40); • }
- 6. Numerical based on Breshenham’s Circle generation algorithm (x,y) (y,x) (-x,y) (-y,x) (-x,-y) (-y,-x) (x,-y) (y,-x) (p<0) P=p+4x+6; x=x+1 (p>=0) P=p+4(x-y)+10 x=x+1, y=y-1 (0,10) (10,0) (-0,10) (-10,0) (-0,-10) (-10,-0) (0,-10) (10,-0) P=-17 (1,10) (10,1) (-1,10) (-10,1) (-1,-10) (-10,-1) (1,-10) (10,-1) P= -7 (2,10) (10,2) (-2,10) (-10,2) (-2,-10) (-10,-2) (2,-10) (10,-2) P=7 (3,9) (9,3) (-3,9) (-9,3) (-3,-9) (-9,-3) (3,-9) (9,-3) P=-7 (4,9) (9,4) (-4,9) (-9,4) (-4,-9) (-9,-4) (4,-9) (9,-4) P=15 (5,8) (8,5) (-5,8) (-8,5) (-5,-8) (-8,-5) (5,-8) (8,-5) P=13 (6,7) (7,6) (-6,7) (-7,6) (-6,-7) (-7,-6) (6,-7) (7-6) P=19 (7,6) (6,7) (-7,6) (-6,7) (-7,-6) (-6,-7) (7,-6) (6-7) don’t Draw These Points Because (x>y). Stop Algorithm when X>=Y. Generate Circle when radius is 10 using breshenham’s circle generation algorithm Let Circle radius is 10 X=0 and y=r or y=10 P=3-2*10; p=-17
- 7. Question • Generate Circle using breshenham’s Circle generation algorithm when radius is 5. (x,y) (y,x) (-x,y) (-y,x) (-x,-y) (-y,-x) (x,-y) (y,-x) (p<0) P=p+4x+6; x=x+1 (p>=0) P=p+4(x-y)+10 x=x+1, y=y-1 (0,5) (5,0) (-0,5) (-5,0) (-0,-5) (-5-0) (0,-5) (5,-0) P=--7 (1,5) (5,1) (-1,5) (-5,1) (-1,-5) (-5,-1) (1,-5) (5,-1) P= 3 (2,4) (4,2) (-2,4) (-4,2) (-2,-4) (-4,-2) (2,-4) (4,-2) P=5 (3,3) (3,3) (-3,3) (-3,3) (-3,-3) (-3,-3) (3,-3) (3,-3) Algorithm will stop when x==y or x>y (don’t calculate next points ) Draw all the calculated points
- 8. THANK YOU!!